Method and apparatus for uniform battery system state of charge management

ABSTRACT

A method and system for generating inverted electrical signals includes a first string of batteries connected in series, each battery having a half-bridge circuit connected in parallel and each having upper switch and lower switches. A first H-bridge circuit is connected in parallel with the first string of batteries, and a triangle wave generator generates a plurality of triangle wave signals at a given amplitude and carrier frequency. The plurality of triangle wave signals have individual triangle wave signals phase-shifted from one another. A modulation wave generator generates a modulation signal at a modulation amplitude and at twice a fundamental frequency that is less than the carrier frequency. A controller compares an instantaneous magnitude of the individual triangle wave signals to an instantaneous magnitude of the modulation signal, and outputs commands to the upper switch of a respective half-bridge circuit based on the comparison.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims priority to Provisional Patent Application62/354,420 filed Jun. 24, 2016, which is hereby incorporated byreference in its entirety.

GOVERNMENT RIGHTS

This invention was made with government support under Grant ECCS-1202133awarded by the National Science Foundation. The government has certainrights in the invention.

BACKGROUND

The United States has traditionally led global efforts to address theever increasing demand for energy and the environmental impact issuescaused by human activities related to energy production and consumption.Other nations, as well, have set ambitious standards to reduce CO₂emissions globally. One promising solution to address such challenges isto electrify transportation for improved fuel efficiency. Such wouldreduce emissions by further implementing clean renewable energy systemsfor electricity generation on a large scale.

Batteries are one of the important technologies for electric drivevehicles (EDVs) that include hybrid electric vehicles (HEVs), plug-inhybrid electric vehicle (PHEVs), and battery electric vehicles (BEVs)(or “EV's” more generally). In multi-battery pack systems such as thoseused in EDVs and utility scale battery storage systems, the batterypacks are charged and discharged with batteries connected in series toachieve a desirable high operating voltage.

However, the characteristics of various battery cells are affected bymany factors such as production variations and differences in agedegradation. Due to differences among different battery modules/cells,some of them are charged or discharged faster than the others in thesame battery chain. The battery module/cell with a lower capacity instring is generally a weak point in the system since it is vulnerable tobeing overcharged or over-discharged, while battery modules/cells withhigher capacity may be only partially utilized. In each charge/dischargecycle, the battery module/cell with the lowest capacity typically mayget weaker and weaker until it fails, which may result in a prematurefailure of the whole battery system. It is then important that allbattery modules/cells operate under a uniform State of Charge (SOC).Known multilevel inverters have been proposed for battery management oflarge battery systems including the battery systems in EDVs and gridconnected large scale battery storage systems.

Multilevel cascaded inverters have been widely used in applications withmedium and/or high voltage levels in general. Modular multilevelconverters (MMCs) are one type of cascaded multilevel converter,characterized by a modular arm design. Modular design can be aneffective means for cost reduction. The advantages of high modularity,ability for direct high voltage connection, and scalability make MMCspromising in many applications. Nevertheless, MMC converters typicallyhave fairly large inductors to suppress the circulating current due tothe voltage difference over the arm inductor. Another issue regardingthis type of converter is the large number of capacitors included foreach module, which can lead to a large converter size. Moreover, forapplications in batteries, the battery modules in an MMC convertertypically have a common DC link, which makes this topology not suitablefor large battery storage systems that include power management ofindividual battery modules.

One known hybrid cascaded multilevel converter was proposed for batterymanagement in electric vehicle applications. By using a multi-carriermagnitude modulation scheme, the individual battery modules/cells in anEV battery pack can be managed. However, the battery modules/cellsconnected in series are typically utilized differently, which decreasesthe system modularity. Additionally, switching devices in differenthalf-bridge circuits may have different switching frequencies, resultingin different device conduction time periods and uneven power lossdistributions. The aforementioned issues can further decrease the systemmodularity. Although some of the issues in the converter can beaddressed by rotating of switching pattern among the switching devices,it adds the complexity to the control and circuit implementation.

In addition, it is challenging to achieve SOC balancing among phases fora uniform SOC operation of an entire system. There is therefore a needto develop a cost-effective way to achieve energy transfer amongdifferent phases. One known method includes a neutral point voltageinjection method for three-phase SOC balancing. However, this may causeasymmetrical terminal quantities of the converter. A negative-sequencevoltage injection method for three-phase energy balancing is also known.However, a negative-sequence voltage injection produces anegative-sequence current, resulting in unbalanced three-phaseoperations in terms of electrical quantities.

Thus, there is tremendous interest to improve SOC battery management.

BRIEF SUMMARY OF THE INVENTION

An electrical converter includes a first string of individual batteriesconnected in series, each individual battery having a half-bridgecircuit connected in parallel, each half-bridge circuit including anupper switch and a lower switch, a first H-bridge circuit connected inparallel with the first string of individual batteries, a triangle wavegenerator that generates a plurality of triangle wave signals at a givenamplitude and carrier frequency, the plurality of triangle wave signalshaving individual triangle wave signals phase-shifted from one another,a modulation wave generator that generates a modulation signal for eachhalf-bridge circuit, and a controller. The controller compares aninstantaneous magnitude of a respective individual triangle wave signalto an instantaneous magnitude of a respective modulation signal, outputsa first command to the upper switch of a respective half-bridge circuitif the respective comparison is positive, and a second command to theupper switch of a respective half-bridge circuit if the respectivecomparison is negative, determines a respective modulation index foreach individual battery based on each respective modulation signal andon the respective individual triangle wave signal, and regulates anamount of power charged to and discharged from each individual batteryby controlling each respective modulation index for each half-bridgecircuit by effecting the respective modulation signal, each modulationindex based on a state-of-charge (SOC) of each individual and respectivebattery.

A method of generating inverted electrical signals includes connecting aplurality of individual batteries together in series into a first stringof individual batteries, connecting half-bridge circuits in parallel toeach of the plurality of individual batteries, each half-bridge circuithaving an upper switch and a lower switch, connecting a first H-bridgecircuit in parallel with the first string of individual batteries,generating a plurality of triangle wave signals at a given amplitude andcarrier frequency, each being phase-shifted from the other, andgenerating a modulation signal for each half-bridge circuit. The methodfurther includes comparing an instantaneous magnitude of a respectiveindividual triangle wave signal to an instantaneous magnitude of arespective modulation signal, outputting a first command to the upperswitch of a respective half-bridge circuit if the respective comparisonis positive, and a second command to the upper switch of a respectivehalf-bridge circuit if the respective comparison is negative,determining a respective modulation index for each individual batterybased on each respective modulation signal and on the respectiveindividual triangle wave signal, and regulating an amount of powercharged to and discharged from each individual battery by controllingeach respective modulation index for each half-bridge circuit, whichincludes controlling the respective modulation signal with respect tothe respective individual triangle wave signal for each individualbattery, each modulation index based on a state-of-charge (SOC) of eachindividual and respective battery.

A non-transitory computer-readable medium tangibly embodyingcomputer-executable instructions of a program being executable by ahardware processor of a computing device with a user interface toprovide operations to generate a plurality of triangle wave signals at agiven amplitude and carrier frequency, each being phase-shifted from theother, generate a modulation signal for each of a plurality ofhalf-bridge circuits, compare an instantaneous magnitude of a respectiveindividual triangle wave signal to an instantaneous magnitude of arespective modulation signal, output a first command to an upper switchof a half-bridge circuit if the comparison is positive, and a secondcommand to the upper switch of a half-bridge circuit if the comparisonis negative, determine a respective modulation index for individualbatteries of a plurality of batteries based on a magnitude of eachrespective modulation signal and based on a magnitude of the respectiveindividual triangle wave signal, and regulates an amount of powercharged to and discharged from each individual battery by controllingeach respective modulation index for each half-bridge circuit, and bycontrolling the respective modulation signal with respect to therespective individual triangle wave signal for each individual battery,each modulation index based on a state-of-charge (SOC) of eachindividual and respective battery. The plurality of individual batteriesare connected together in series into a first string of individualbatteries, and the half-bridge circuits are connected in parallel toeach of the plurality of individual batteries, each half-bridge circuithaving the upper switch and a lower switch, and a first H-bridge circuitis connected in parallel with the first string of individual batteries.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a circuit that includes a half-bridge blockinterfaced to an individual module/cell.

FIG. 2 illustrates an exemplary configuration of a nine-level HierarchalCascaded Multilevel Converter (HCMC) inverter.

FIG. 3 illustrates a phase-shifted scheme for circuit of FIG. 2.

FIG. 4 illustrates an alternating dc link voltage Vdc of the circuit ofFIG. 2.

FIG. 5 illustrates an exemplary three-phase twenty five-level HCMC withtwo hierarchical cascaded levels.

FIGS. 6(a)-(c) illustrate different cases of modulation indexes toregulate battery power and/or bypass the battery module/cell.

FIG. 7 illustrates a six-switch balancing circuit (SSBC) for controllinga three-phase, thirty-three level HCMC inverter.

FIG. 8 shows reference voltage waveforms of the SSBC of FIG. 7.

DETAILED DESCRIPTION

Referring now to the discussion that follows and the drawings,illustrative approaches to the disclosed systems and methods aredescribed in detail. Although the drawings represent some possibleapproaches, the drawings are not necessarily to scale and certainfeatures may be exaggerated, removed, or partially sectioned to betterillustrate and explain the present disclosure. Further, the descriptionsset forth herein are not intended to be exhaustive, otherwise limit, orrestrict the claims to the precise forms and configurations shown in thedrawings and disclosed in the following detailed description.

Disclosed is a new topology of a cascaded multilevel converter, calledHierarchal Cascaded Multilevel Converter (HCMC). The disclosed topologyis a hybrid combination of both H-bridge and half-bridge converterswhich are cascaded at two hierarchical levels, i.e. the H-bridge leveland half-bridge level. A phase-shifted pulse-width modulated (PWM)technique is disclosed to control the switching frequency and conductiontime for the switching devices in the half-bridge circuits to achieve anequal utilization of battery modules/cells. The disclosed converter hasthe features of high voltage and high power application capability andmodular design for cost reduction and reliability improvement. A uniformState of Charge (SOC) profile is achieved via the disclosed converterwithout adding additional balancing circuits. Furthermore, failedindividual battery modules/cells can be bypassed via the converterwithout bringing down the whole battery system.

For large scale battery systems, cell/module balancing is important toprotect the weaker batteries while fully utilizing the full capacity ofthe whole battery system. In the disclosed converter, a uniform SOCoperation is achieved and maintained continuously by controllingindividual battery modules/cells without any energy shuffling among thebatteries or energy disposal.

To control individual battery modules/cells, a HCMC that includeshalf-bridge converter blocks and H-bridge blocks is disclosed. FIG. 1shows a circuit 100 that includes a half-bridge block 102 that isinterfaced to an individual module/cell 104 and manages module/cell 104.Accordingly, individual modules and cells can be managed separatelythrough half-bridge blocks using circuit 100. Half-bridge circuits suchas circuit 100 are cascaded in series and then connected to an H-bridgecircuit to form a hybrid multilevel converter, as will be furtherillustrated.

FIG. 2 illustrates an exemplary inverter circuit or configuration 200 ofa nine-level HCMC having only one H-bridge 202 in a single phase.H-bridge 202 in circuit 200 is used to alternate a dc link outputvoltage of cascaded half-bridge blocks 204, with all half-bridge blocks204 connected in parallel to isolated individual string of batteries 206that are connected in series. In FIG. 2, upper switches S₁, S₂, S₃, andS₄ in cascaded half-bridge blocks 204 conduct, and an output voltage ofeach of the half-bridge blocks is V_(h1)=V_(h2)=V_(h3)=V_(h4)=E. Hence,the resultant dc voltage is Vdc=V_(h1)+V_(h2)+V_(h3)+V_(h4)=4E. Theoutput phase voltage of the HCMC converter is an alternating voltageswitched from +4E to −4E by using H-bridge 202, which operates at afundamental frequency of a reference signal, and is connected inparallel with string of batteries 206. The other four voltage levels ofthe dc link are 3E, 2E, E, and 0, which correspond to the variousswitching states summarized in Table I, and which likewise are switchedas either positive or negative using H-bridge 202. It can be observedfrom Table I that some voltage levels can be obtained by more than oneswitching state. For example, the voltage level 2E can be produced bysix sets of different switching states which provide a great flexibilityfor switching pattern.

In general, the number of voltage levels in a HCMC multilevel invertercan be found from Eqn. 1:m=2h+1,  Eqn. 1,where h is the number of half-bridge cells per phase. And, although anexemplary nine-level HCMC is illustrated, it is contemplated that anynumber of levels of HCMC may be employed. For instance, in the basiccell (cascaded half-bridge), the number of levels is proportional tonumber of cascaded half-bridge converters, which is determined by therated voltages of both battery modules and the overall output voltagethat is desired. Theoretically there is no limit, but practically thenumber of levels may be limited by circuit components such as the DSPchip used.

The voltage level m is therefore an odd number for the HCMC multilevelinverter. Thus, in the disclosed example of FIG. 2, h is 4 and m istherefore 9. It is in the same pattern as that of traditional cascadedH-bridge (CHB) multilevel inverters while in other multilevel topologiessuch as diode-clamped inverters the voltage level can be either an evenor odd number.

TABLE 1 DC Link Switching State voltage S₁ S₂ S₃ S₄ V_(h1) V_(h2) V_(h3)V_(h4) 4 E 1 1 1 1 E E E E 3 E 0 1 1 1 0 E E E 1 0 1 1 E 0 E E 1 1 0 1 EE 0 E 1 1 1 0 E E E 0 2 E 0 0 1 1 0 0 E E 1 0 0 1 E 0 0 E 1 1 0 0 E E 00 1 0 1 0 E 0 E 0 0 1 0 1 0 E 0 E 0 1 1 0 0 E E 0 E 1 0 0 0 E 0 0 0 0 10 0 0 E 0 0 0 0 1 0 0 0 E 0 0 0 0 1 0 0 0 E 0 0 0 0 0 0 0 0 0

Generally, a traditional and known multilevel inverter with m voltagelevels may have (m−1) triangular carriers. In contrast, the cascadedhalf-bridge cells in the disclosed HCMC inverter include only (m−1)/2triangular waves, as will be further illustrated. A phase-shifted PWMmodulation scheme is developed for the disclosed HCMC. By using aphase-shifted multicarrier modulation, the triangular carriers have thesame frequency and the same amplitude, but with a phase shift (φ)between any two adjacent carrier waves, given by Eqn. 2:

$\begin{matrix}{{\varphi = \frac{360{^\circ}}{m - 1}},} & {{Eqn}.\mspace{14mu} 2}\end{matrix}$where m is the number of output voltage levels in the HCMC.

For the cascaded half-bridge converter blocks, a modulation signal V_(m)is the absolute value of a reference voltage and the gate signals aregenerated by comparing the absolute value of the reference voltage wavewith the carrier signals. FIG. 3 shows the principle of thephase-shifted scheme for circuit 200 of FIG. 2, the nine-level HCMCconverter. The carrier waves V_(cr1), V_(cr2), V_(cr3), and V_(cr4) areused to generate the gate signals for the upper switches of the cascadedcells 204 in FIG. 2. The gate signals S₁ ⁻, S₂ ⁻, S₃ ⁻, and S₄ ⁻ for thelower switches in the cascaded half-bridge are not shown since theseswitches operate in a complementary way with respect to theircorresponding upper switches. That is, for example when switch S₁ isclosed then corresponding switch S₁ ⁻ is opened.

As shown in FIG. 3, the gate signals for the upper switches S₁, S₂, S₃,and S₄ in the corresponding cascaded blocks 204 are generated bycomparing V_(cr1), V_(cr2), V_(cr3), and V_(cr4) with V_(m). Hence, theresultant voltages V_(h1), V_(h2), V_(h3), and V_(h3) are switchedbetween zero and E during the half cycle at the fundamental frequency.The modulation index can be calculated as:m _(i) =V _(mp) /V _(crp),  Eqn. 3,where V_(mp) and V_(crp) are the peak amplitudes of V_(m) and V_(cr),respectively.

The dc link voltage can be readily obtained as:V _(dc) =V _(h1) +V _(h2) +V _(h3) +V _(h4),  Eqn. 4.

For instance, referring still to FIG. 3, at a given phase angle “X”,300, V_(cr1) and V_(cr2), respectively labeled as elements 302 and 304,are above, or have a greater magnitude, than modulation signal V_(m)306. Since modulation signal V_(m) is less than each of V_(cr1) andV_(cr2) at phase angle “X”, then voltages V_(h1) and V_(h2) are eachzero, as indicated by elements 308, 310. At the same phase angle “X”,300, modulation signal V_(m) is greater than each of V_(cr3) andV_(cr4), as indicated at 303, 305, thus voltages V_(h3) and V_(h4) areeach “E”, as indicated by elements 312, 314. Accordingly, at phase angle“X”, 300, V_(dc)=0+0+E+E=2E, as illustrated by element 316. Based on theabove example at phase angle “X”, 300, it is recognized that, asmodulation signal V_(m) is swept through 27, an overall pattern 318 ofoutput results. That is, depending on the phase angle of modulationsignal V_(m), its given amplitude with respect to each of V_(cr1),V_(cr2), V_(cr3), and V_(cr4) correspondingly determines whether each ofvoltages V_(h1), V_(h2), V_(h3), and V_(h3) is 0 or E. Switch patterns,as discussed above, thereby result in an overall set of options thatcorrespond with Table 1 above.

Accordingly, referring back to FIG. 2, inverter circuit 200 includes acontroller 208 that is coupled to a triangle wave generator 210 andhaving a carrier frequency, as well as a modulation wave generator 212for generating a modulation signal at a modulation amplitude and attwice a fundamental frequency that is less than the carrier frequency.That is, as shown in FIG. 3, modulation signal V_(m) 306 is twice thefundamental frequency having positive amplitudes. And, as discussedabove, in the example illustrated, triangle wave generator 210 in thiscase generates the four V_(cr1), V_(cr2), V_(cr3), and V_(cr4) withappropriate phase offsets or phase-shifts from each, each at a givenamplitude and carrier frequency. Modulation wave generator 212correspondingly generates modulation signal V_(m), at a given amplitudeand at a fundamental frequency that is less than that of the carrierfrequency. A comparator circuit 214 compares each of V_(cr1), V_(cr2),V_(cr3), and V_(cr4) to modulation signal V_(m) as described above. Eachis correspondingly output to respective upper switches S₁, S₂, S₃, andS₄, with lower switches S₁ ⁻, S₂ ⁻, S₃ ⁻, and S₄ ⁻ operating in acomplementary fashion, resulting in overall pattern 318 of FIG. 3. Thatis, by operating in a complementary fashion, when one of the switches isopen, the other is closed, and vice versa.

Thus, controller 208 1) compares an instantaneous magnitude of each ofthe individual triangle wave signals V_(cr1), V_(cr2), V_(cr3), andV_(cr4) to an instantaneous magnitude of the modulation signal V_(m)306, and 2) outputs a first command to the upper switch S₁, S₂, S₃, andS₄ of a respective half-bridge circuit 206 if the respective comparisonis positive, and a second command to the upper switch S₁, S₂, S₃, and S₄of a respective half-bridge circuit 206 if the respective comparison isnegative.

Also, it is contemplated that FIG. 3 is used to illustrate the conceptof phase-shifted PWM modulation for the disclosed inverter. Each of thehalf bridge in FIG. 2, however, can be controlled to have a differentmodulation index so that the charging/discharging power to eachindividual battery cell can be controlled. Therefore, the disclosedmethod and apparatus work when the battery cells either have the sameSOC or different SOC. When the battery cells have different SOC, powermagnitudes to individual cells will be different. And, as will befurther disclosed, if the battery packs in the overall three phases haveoverall different SOC values, then the three phase power will bedifferent (unbalanced) as well.

As discussed, however, an H-bridge circuit is also employed to modulatethe output signal to have both positive and negative portions, resultingin an approximate sinusoidal output. That is, the H-bridge circuit isused to alternate the dc link voltage Vdc as shown in FIG. 4. The outputvoltage signal 400 is the nine-level HCMC phase voltage under thecondition, in this example, of a 60 Hz fundamental frequency V_(m), a180 Hz carrier frequency corresponding to each of V_(cr1), V_(cr2),V_(cr3), and V_(cr4), and a modulation index m_(i) at 0.95. It can beclearly seen that the converter phase voltage waveform is formed by ninevoltage steps: +4E, +3E, +2E, +E, 0, −E, −2E, −3E, and −4E. Themagnitude of voltage step is only E during the switching between voltagelevels, which leads to a low voltage stress.

An exemplary three-phase twenty five-level HCMC 500 is shown in FIG. 5.Illustrated are four cascaded half-bridge converters 502 in eachH-bridge converter block 504 and there are 3 H-bridge converters 504cascaded for each single phase 506. Output of the cascaded half-bridgeconverters 502 is connected to a dc side of each H-bridge converter 508.In this topology, each battery module/cell, such as individual batteries206 of FIG. 2, can either produce an output voltage E, or beingbypassed, which can be achieved by simply controlling the switches ineach respective half-bridge converter for each battery module/cell asdescribed above.

The charge and discharge power to each battery module/cell can becontrolled by controlling the modulation index, which is discussedabove. The H-bridge function is to alternate the output of the dc linkto produce ac waveforms at output terminals V_(A), V_(B), and V_(C). Theswitches in the H-bridge converters handle relatively high voltage andpower levels, but are switched at a much lower frequency (i.e., thefundamental frequency). On the other hand, the switches in eachhalf-bridge converter work under lower voltage and power and can beswitched much faster. Therefore, MOSFETs can be selected as the switchesfor the half-bridge blocks while insulated-gate bipolar transistors(IGBTs) can be chosen for the H-bridge converter blocks in the HCMC.Compared to traditional H-bridge multilevel converters, the number ofswitching devices is reduced, especially for large battery systems,which simplifies control drive circuits, reduces total cost, andachieves a smaller size of converter.

The charge and discharge power control of an individual batterymodule/cell is achieved through the control over the half-bridgeconverter connected to the module/cell. That is, charge and dischargepower can be regulated by controlling the modulation index m_(i) of theswitching device of each half-bridge converter, such as cascadedhalf-bridge blocks 204 of FIG. 2. Instantaneous charge/discharge powerof the battery module/cell is given by:P _(cell,i)(t)=S _(upper,i)(t)×E _(i) ×I _(dc),  Eqn. 5,

where S_(upper,i) is the ith battery module/cell upper switch states: 1is ON or 0 is OFF; E_(i) and I_(dc) are the voltage of the individualbattery module/cell and the battery current of the whole string,respectively. The average power of a battery module/cell is:P _(cell,i) =m _(i) ×E _(i) ×I _(dc),  Eqn. 6.

Hence, the charge or discharge power of each battery module/cell iscontrolled by regulating m_(i) of the corresponding half-bridgeconverter. A continuous uniform SOC operation can be achieved in thisway. For example, if a module/cell has a relatively high SOC, it can becontrolled to be charged less and/or discharged more. On the other hand,for a module/cell with a relatively lower SOC, it can be controlled tobe charged more and/or discharged less.

FIGS. 6(a)-(c) show different cases of m_(i) where it is used toregulate battery power and/or bypass the battery module/cell. Forexample, in a discharging process, a battery module/cell with a higherSOC can be discharged more even with an over-modulated amplitude orindex m_(i)>1, shown in FIG. 6(a) 600. Other battery modules/cells witha lower SOC can be controlled to be discharged less with a lowermodulation index, 0<m_(i)<1, shown in FIG. 6(b) 602. In the chargingprocess, a similar strategy can be carried out. When one or moremodules/cells need to be bypassed, the upper switching devices of thehalf-bridge converters of these battery modules/cells can be turned OFFby simply applying m_(i)=0, as shown in FIG. 6(c) 604 without affectingother modules/cells. However, in this case, the overall phase outputvoltage with bypassed modules/cells will be reduced. The half-bridgeconverters of the other healthy battery modules/cells can be controlledto generate a higher voltage to compensate this voltage drop until thedamaged battery modules/cells are replaced. Nevertheless, during thatperiod of time, the whole system may be operated at a de-rated power andenergy level. Further, the SOC is measured in real time, and can bedetermined by actual applications for time frames such as 10 secondintervals, 1 minute intervals, 10 minute intervals, etc. The modulationindex (or Vm you may use) is a function of SOC.

The overall (charge or discharge) power can be regulated by controllingthe overall output AC voltage, i.e. the magnitude and phase angle. Thereference signal equations of the three phase system shown in FIG. 5 aregiven by:V _(A) =V _(m,A)|sin(ωt+β)|,  Eqn. 7,V _(B) =V _(m,B)|sin(ωt−120+β)|,  Eqn. 8,V _(C) =V _(m,C)|sin(ωt+120β)|,  Eqn. 9.

In steady state, V_(m,A), V_(m,B), V_(m,C) should be the same tomaintain a balanced three phase system, which can done by controllingthe modulation index m_(i) for each battery module, on top of theuniform SOC management for all batteries in the strings. The energyutilization ratio can be improved while over-charge/discharge is avoidedvia controlling the individual battery modules/cells, as well asregulating the overall power. For example, assuming that the phase angleof the grid voltage is 0°, a positive β will bring the converter intodischarge mode while a negative β will set the converter at a chargemode.

The overall power demand can be decomposed into the commands at theindividual battery module/cell level as:

$\begin{matrix}{{P_{{cell},i}^{*} = {\frac{P_{tot}}{N} + {\Delta\; P_{{cell},i}}}},} & {{Eqn}.\mspace{14mu} 10}\end{matrix}$where P_(tot) is the overall power demand; P*_(cell,i) is the referencevalue for the ith battery module/cell; Nis the total number ofmodules/cells in the system; and ΔP_(cell,i) is the power adjustment forthe uniform SOC management and

${\sum\limits_{i = 1}^{N}\;{\Delta\; P_{{cell},i}}} = 0.$

Thus, FIG. 5 shows a first leg of batteries 506 that includes a firststring of batteries connected in series with a second string ofbatteries 504, the second string of batteries are connected in series.The strings of batteries each have an H-bridge circuit 508 connected inparallel with a respective string 504. Respective half-bridge circuitsare connected in parallel, respectively, with individual batteries inthe strings of batteries. Controller 208 outputs commands to upperswitches within the strings of half-bridge circuits to open and closethe upper switches within the string of half-bridge circuits.

Accordingly, disclosed is a phase-shifted modulation based modulardesign. Phase-shifted modulation is used in the disclosed converter.Phase-shifted modulation enables the feature of modularity of thedisclosed converter. That is, the switching devices in the differenthalf-bridge circuits have the same switching frequencies, and the samedevice conduction times. The design includes even power lossdistributions, though the switching devices can be controlled to work atdifferent power levels. Modularity makes the system easier to implement,less costly to maintain, and more reliable to operate. In addition, highvoltage and high power is achieved by hierarchical cascaded connectionof smaller switching devices. The disclosed converter is cascaded at twolevels: the half bridge level and the H-bridge level. The disclosedconverter can be used for any voltage level (even over 110 kV) withoutusing transformers.

That is, disclosed is a Hierarchal Cascaded Multilevel Converter (HCMC)for high voltage and high power battery systems to achieve continuousuniform SOC operation. The disclosed HCMC has a hybrid structure ofhalf-bridge converters and H-bridge converters and the voltage can becascaded to reach a high level at two hierarchical levels: thehalf-bridge level and the H-bridge level. The phase-shifted PWMmodulation technique achieves the same switching frequency andconduction time for the switching devices in the half-bridge circuits toachieve an equal utilization of battery modules/cells in general. Theconverter has the features of high voltage and high power applicationcapability and modular design for cost reduction and reliabilityimprovement. Continuous uniform SOC operation is achieved via thedisclosed converter without adding additional balancing circuits.Furthermore, the disclosed converter has a reconfigurable topology andan adaptive control scheme, such that failed individual batterymodules/cells can be bypassed without bringing down the whole batterysystem. Also, individual battery modules can be managed independently oncharge/discharge power, and bypass control while the overall performancerequirement is also met.

Disclosed herein, also, is a three-phase SOC equalizing circuit, calledsix-switch energy-level balancing circuit, which can be used to realizeuniform SOC operation for full utilization of the battery capacity in athree-phase battery energy storage system (BESS) while keeping balancedthree-phase operation. A sinusoidal PWM modulation scheme is disclosedto control power transferring between phases in a cascaded inverter,such as that disclosed herein. Also, a phase-shifted PWM modulationtechnique is developed for a BESS to control the same switchingfrequency for switching devices.

For a large scale three-phase battery system that includes separatebattery packs for individual phases, the battery packs in differentphases typically, or often, have different capacities. As a result, evenif a uniform SOC can be maintained for the batteries within each phase,there can be substantial SOC differences among phases, which decreasethe whole system's battery utilization and the system reliability.Therefore, three-phase uniform SOC operation is important to utilize thefull capacity of the whole battery system. In the disclosed circuit, auniform three-phase balanced SOC operation is achieved for the wholesystem. Although the disclosed phase-to-phase balancing circuit alsoworks for other types of cascaded inverters, the following discussion isparticular to a hierarchical cascaded multilevel converter (HCMC), asdiscussed above.

A six-switch balancing circuit (SSBC) is disclosed, which is at thebottom level of the cascaded converter and provides a path for powertransfer between the phases, shown in FIG. 7. A common battery module(i.e., a common DC source) is used in the three-phase SSBC. In additionto the capability of transferring power between phases, the disclosedSOC balancing circuit can be used as a three-phase inverter and hence apart of the HCMC to increase the system power/energy ability as needed.

The disclosed structure involves two SOC balancing levels (i.e., phaseand phase-to-phase SOC balancing levels) and hence utilizes the fullcapacity of a BESS. To achieve a first level, the HCMC is used whichincludes half-bridge and H-bridge converter blocks to control power ofindividual battery modules/cells, as described above. FIG. 7 shows anexample thirty-three level HCMC 700, with the following discussionfocused on uniform SOC operations among phases 702, 704, 706, which isachieved through the disclosed SSBC circuit 708.

The three-phase circuit of SSBC 708 is realized by adding threehalf-bridge converters 710, 712, 714 (i.e., one half-bridge per phase)that are connected to the same common DC link 716, as shown in FIG. 7.The DC source or link 716 can be charged/discharged through the upperswitching devices (i.e., S_(a+), S_(b+), and S_(c+)) in the half-bridgeconverters. Moreover, the SSBC can be considered as a bottom levelcascaded block in the HCMC, if needed.

Real and reactive powers delivered (under discharging) to or provided(under charging) by a grid are determined by an amplitude and angle ofan output voltage of the cascaded inverter. For a given reference valueof real and reactive power P and Q, the magnitude (V_(s)) and phaseangle (β) of the inverter output can be obtained as:

$\begin{matrix}{{V_{s} = \sqrt{{\frac{Z^{2}}{U^{2}}\left( {P^{2} + Q^{2}} \right)} + U^{2} + {2{PZ}\;{\cos\left( \theta_{z} \right)}} + {2{QZ}\;{\sin\left( \theta_{z} \right)}}}},{and}} & {{Eqn}.\mspace{14mu} 11} \\{\mspace{76mu}{{\beta = {\theta_{z} - {\cos^{- 1}\left( {\frac{ZP}{{UV}_{s}} + {\frac{U}{V_{s}}\cos\mspace{14mu}\left( \theta_{z} \right)}} \right)}}},}} & {{Eqn}.\mspace{14mu} 12}\end{matrix}$where Z=√{square root over (R_(s) ²+X_(s) ²)}, θ_(Z)=tan⁻¹(R_(s)/X_(s)).R_(s)+jX_(s) is the coupling impedance and the grid voltage is assumedto be U∠0°. β will be negative when the grid charges battery.

The overall output voltage phasor ({right arrow over (V)}_(s)=V_(s)∠β)of the HCMC inverter is realized by the control of individual batterymodules/cells. The charge and discharge of an individual batterymodule/cell (battery module i in phase x, x=a, b, c) is achieved throughthe control over the half-bridge converter connected to the module/cell(E_(i,x)). The charge and discharge power can be regulated bycontrolling the modulation index m_(i,x) (x=a, b, c) of the switchingdevices in each half-bridge converter, as shown in FIG. 7. Fordischarging control (delivering power back to the grid):

$\begin{matrix}{{m_{i,x} = \frac{V_{{sm},x}\mspace{14mu}{SOC}_{i,x}}{E_{i,x}{\sum\limits_{i = 1}^{N_{x}}\;{SOC}_{i,x}}}},{x = a},b,c,} & {{Eqn}.\mspace{14mu} 13}\end{matrix}$where V_(sm,x) is the peak value of phase x of the inverter outputvoltage. E_(i,x) is the terminal voltage of battery module i in phase x.N_(x) is the total number of battery modules in series for phase x.

In steady state, V_(sm,a), V_(sm,b), and V_(sm,c) should be the same fora balanced three-phase operation while β angle is used to regulate theoverall power. For example, assuming that the phase angle of the gridvoltage is 0°, a positive β will bring the cascaded multilevel inverterinto discharge mode while negative β will set the converter at a chargemode.

For charging control, the corresponding modulation index for batterymodule i in phase x can be obtained in a similar way:

$\begin{matrix}{{m_{i,x} = \frac{{V_{{sm},x}\mspace{14mu} 1} - {SOC}_{i,x}}{E_{i,x}{\sum\limits_{i = 1}^{N_{x}}\;\left( {1 - {SOC}_{i,x}} \right)}}},{x = a},b,{c.}} & {{Eqn}.\mspace{14mu} 14}\end{matrix}$

The half-bridge converters h_(a), h_(b), and h_(c) in FIG. 7 arecontrolled based on the average SOC value of the batteries in each phasewhich can be given by:

$\begin{matrix}{{{SOC}_{x} = {{\frac{1}{N}{\sum\limits_{x_{i} = 1}^{N_{x}}\;{{SOC}_{x_{i}}\mspace{14mu} x}}} = a}},b,c,} & {{Eqn}.\mspace{14mu} 15}\end{matrix}$where N_(x) is the total number of battery modules/cells per phase andthe average SOC for the whole system can be expressed as:SOC=⅓(SOC_(a)+SOC_(b)+SOC_(c)),  Eqn. 16.

The power of charge/discharge processes can be regulated by controllingthe modulation indices k_(a), k_(b), and k_(c) of the upper switchingdevices S_(a+), S_(b+), and S_(c+), respectively. When the main batterysystem is under discharge, the modulation indices for the threehalf-bridge converters in the SSBC can be determined as:

$\begin{matrix}{{k_{x} = \frac{\overset{\_}{SOC} - {SOC}_{x}}{\Delta\;{SOC}_{\max}}},{x = a},b,c,} & {{Eqn}.\mspace{14mu} 17}\end{matrix}$where

${{\Delta\;{SOC}_{\max}} = {\max\limits_{x}\left( {{SOC}_{x} - \overset{\_}{SOC}} \right)}},{x = a},b,{c.}$It should be noted that the batteries in each phase are managed by theHCMC to operate at its uniform SOC, i.e., SOC_(x), x=a, b, c, asdiscussed in the previous sub-section.

When the main battery system is under charge, the concept remains thesame. Under this situation, the modulation indices for the threehalf-bridge converters in the SSBC are given as follows:

$\begin{matrix}{{k_{x} = \frac{{SOC}_{x} - \overset{\_}{SOC}}{\Delta\;{SOC}_{\max}}},{x = a},b,{c.}} & {{Eqn}.\mspace{14mu} 18}\end{matrix}$

The modulation index k_(x) for each phase leg in the SSBC can benegative. When k_(x) is negative, the reference voltage waveform forS_(x+) in the corresponding half-bridge converter (i.e., phase x in theSSBC) is 180° out of phase compared to the reference voltage for phase xin the main HCMC. On the other hand, if k_(x) is positive, then thereference voltage waveform for S_(x+) in the corresponding half-bridgeconverter (i.e., phase x in the SSBC) is in phase with the referencevoltage for phase x in the main HCMC. For example, consider a case thatthe main battery system is under discharge, and SOC_(a)>SOC_(c)>SOC_(b)and SOC_(c)=SOC. In this case, k_(a)=−1, k_(b)=1, and k_(c)=0. Theenergy will be transferred from phase A to phase B until a uniform SOCis achieved for all the three phases.

FIG. 8 shows the reference voltage waveforms of the SSBC. It can be seenthat the reference voltage waveform for S_(a+) in the half-bridgeconverter of h_(a) 800 is 180° out of phase from the reference voltagewaveform of phase A 802 in the main HCMC. The reference voltage waveformfor S_(b+) in the half-bridge converter of h_(b) 804 is in phase withthe reference voltage waveform of phase B 806 in the HCMC. As a result,in addition to the regular phase power, the batteries in phase A of themain HCMC are to be discharged more by also charging the battery in theSSBC. On the other hand, the batteries in phase B of the main HCMC areto be discharged less since the battery in the SSBC is in phase with itto provide support to the phase. Note that the battery in the SSBC doesnot store or discharge energy in a cycle. It basically transfers theenergy from phase A to phase B in the main system. This will ensurethat:

$\begin{matrix}{{{\sum\limits_{x}k_{x}} = 0},{x = a},b,{c.}} & {{Eqn}.\mspace{14mu} 19}\end{matrix}$

The instantaneous charge/discharge power of the battery in the SSBC isgiven by:p _(dc)(t)=(S _(a)(t)×I+S _(b)(t)×I+S _(c)(t)×I)×V _(dc),  Eqn. 20,where S_(a), S_(b), and S_(c) are the switch states of upper switchesS_(a+), S_(b+), and S_(c+), respectively. V_(dc) and I are the dc sourcevoltage and the current of each half-bridge converter in the SSBC,respectively. Thus, the average power of the SSBC is:P _(dc)=(k _(a) ×I+k _(b) ×I+k _(c)×1)×V _(dc)=0,  Eqn. 21.

This disclosure includes an improved HCMC inverter topology for managinglarge scale battery systems with phase-to-phase SOC balancingcapability. Uniform SOC operation for the whole system is achieved via atwo-level SOC balancing scheme: the phase SOC balancing andphase-to-phase SOC balancing. The battery modules/cells in each phaseare managed by the main HCMC inverter to operate at its uniform SOC.When the whole battery system is under unbalance of SOC among phases,the SSBC circuit can be used to transfer power between phases. Inaddition to the function of equalizing SOC, the disclosed energy-levelbalancing circuit can be used to increase the system capacity. Harmoniccomponents can be reduced by increasing the carrier frequency of theSSBC circuit. In addition to the HCMC, the disclosed phase-to-phasebalancing circuit and the corresponding control strategy can be readilyused for other cascaded multilevel battery inverters to achievephase-to-phase SOC balancing.

Computing devices such as controller 208 may include a computer that mayemploy any of a number of computer operating systems known to thoseskilled in the art, including, but by no means limited to,microprocessor systems, such as those manufactured by Motorola andIntel. The controller 208 may also employ known versions and/orvarieties of the Microsoft Windows® operating system, the Unix operatingsystem (e.g., the Solaris® operating system distributed by OracleCorporation of Redwood Shores, Calif.), the AIX UNIX operating systemdistributed by International Business Machines of Armonk, N.Y., and theLinux operating system. Computing devices may include any one of anumber of computing devices known to those skilled in the art,including, without limitation, a computer workstation, a desktop,notebook, laptop, or handheld computer, or some other computing deviceknown to those skilled in the art.

Computing devices such as the foregoing generally each includeinstructions executable by one or more computing devices such as thoselisted above. Computer-executable instructions may be compiled orinterpreted from computer programs created using a variety ofprogramming languages and/or technologies known to those skilled in theart, including, without limitation, and either alone or in combination,Java™, C, C++, Visual Basic, Java Script, Perl, etc. In general, aprocessor (e.g., a microprocessor) receives instructions, e.g., from amemory, a computer-readable medium, etc., and executes theseinstructions, thereby performing one or more processes, including one ormore of the processes described herein. Such instructions and other datamay be stored and transmitted using a variety of known computer-readablemedia.

A computer-readable medium includes any medium that participates inproviding data (e.g., instructions), which may be read by a computer.Such a medium may take many forms, including, but not limited to,non-volatile media, volatile media, and transmission media. Non-volatilemedia include, for example, optical or magnetic disks and otherpersistent memory. Volatile media include dynamic random access memory(DRAM), which typically constitutes a main memory. Transmission mediainclude coaxial cables, copper wire and fiber optics, including thewires that comprise a system bus coupled to the processor. Transmissionmedia may include or convey acoustic waves, light waves andelectromagnetic emissions, such as those generated during radiofrequency (RF) and infrared (IR) data communications. Common forms ofcomputer-readable media include, for example, a floppy disk, a flexibledisk, hard disk, magnetic tape, any other magnetic medium, a CD-ROM,DVD, any other optical medium, punch cards, paper tape, any otherphysical medium with patterns of holes, a RAM, a PROM, an EPROM, aFLASH-EEPROM, any other memory chip or cartridge, a carrier wave asdescribed hereinafter, or any other tangible medium from which acomputer can read.

It is intended that the scope of the present methods and apparatuses bedefined by the following claims. However, it must be understood that thedisclosed system may be practiced otherwise than is specificallyexplained and illustrated without departing from its spirit or scope. Itshould be understood by those skilled in the art that variousalternatives to the configuration described herein may be employed inpracticing the claims without departing from the spirit and scope asdefined in the following claims. The scope of the disclosure should bedetermined, not with reference to the above description, but shouldinstead be determined with reference to the appended claims, along withthe full scope of equivalents to which such claims are entitled. It isanticipated and intended that future developments will occur in the artsdiscussed herein, and that the disclosed systems and methods will beincorporated into such future examples.

Furthermore, all terms used in the claims are intended to be given theirbroadest reasonable constructions and their ordinary meanings asunderstood by those skilled in the art unless an explicit indication tothe contrary is made herein. In particular, use of the singular articlessuch as “a,” “the,” “said,” etc., should be read to recite one or moreof the indicated elements unless a claim recites an explicit limitationto the contrary. It is intended that the following claims define thescope of the device and that the method and apparatus within the scopeof these claims and their equivalents be covered thereby. In sum, itshould be understood that the device is capable of modification andvariation and is limited only by the following claims.

The invention claimed is:
 1. An electrical converter, comprising: afirst string of individual batteries connected in series, eachindividual battery having a half-bridge circuit connected in parallel,each half-bridge circuit including an upper switch and a lower switch; afirst H-bridge circuit connected in parallel with the first string ofindividual batteries; a triangle wave generator that generates aplurality of triangle wave signals at a given amplitude and carrierfrequency, the plurality of triangle wave signals having individualtriangle wave signals phase-shifted from one another; a modulation wavegenerator that generates a modulation signal for each half-bridgecircuit; and a controller that: compares an instantaneous magnitude of arespective individual triangle wave signal to an instantaneous magnitudeof a respective modulation signal; outputs a first command to the upperswitch of a respective half-bridge circuit if the respective comparisonis positive, and a second command to the upper switch of a respectivehalf-bridge circuit if the respective comparison is negative; determinesa respective modulation index for each individual battery based on eachrespective modulation signal and on the respective individual trianglewave signal; and regulates an amount of power charged to and dischargedfrom each individual battery by controlling each respective modulationindex for each half-bridge circuit by effecting the respectivemodulation signal, each modulation index based on a state-of-charge(SOC) of each individual and respective battery.
 2. The electricalinverter of claim 1, wherein one of the first and second commands is toopen the respective upper switch, and the other of the first and secondcommands is to close the respective upper switch.
 3. The electricalinverter of claim 2, wherein the upper switch and the lower switchoperate complementary to one another.
 4. The electrical inverter ofclaim 1, further comprising a first leg of individual batteries thatincludes the first string of individual batteries connected in serieswith a second string of individual batteries, the second string ofindividual batteries connected in series, the second string ofindividual batteries having a second H-bridge circuit connected inparallel and having respective second string half-bridge circuits inparallel respectively with the individual batteries within the secondstring of individual batteries, wherein the controller outputs commandsto the upper switches within the second string half-bridge circuits toopen and close the upper switches within the second string half-bridgecircuits.
 5. The electrical inverter of claim 4, further comprisingsecond and third legs of batteries connected in parallel with the firstleg of individual batteries.
 6. A method of generating invertedelectrical signals, comprising: connecting a plurality of individualbatteries together in series into a first string of individualbatteries; connecting half-bridge circuits in parallel to each of theplurality of individual batteries, each half-bridge circuit having anupper switch and a lower switch; connecting a first H-bridge circuit inparallel with the first string of individual batteries; generating aplurality of triangle wave signals at a given amplitude and carrierfrequency, each being phase-shifted from the other; generating amodulation signal for each half-bridge circuit; comparing aninstantaneous magnitude of a respective individual triangle wave signalto an instantaneous magnitude of a respective modulation signal;outputting a first command to the upper switch of a respectivehalf-bridge circuit if the respective comparison is positive, and asecond command to the upper switch of a respective half-bridge circuitif the respective comparison is negative; determining a respectivemodulation index for each individual battery based on each respectivemodulation signal and on the respective individual triangle wave signal;and regulating an amount of power charged to and discharged from eachindividual battery by controlling each respective modulation index foreach half-bridge circuit, which includes controlling the respectivemodulation signal with respect to the respective individual trianglewave signal for each individual battery, each modulation index based ona state-of-charge (SOC) of each individual and respective battery. 7.The method of claim 6, wherein one of the first and second commands isto open the respective upper switch, and the other of the first andsecond commands is to close the respective upper switch.
 8. The methodof claim 7, further comprising operating the upper switch and the lowerswitch complementary to one another.
 9. The method of claim 6, whereineach battery has a respective state-of-charge (SOC) different from oneanother.
 10. The method of claim 9, further comprising: connecting asecond string of individual batteries in series, each having respectivesecond string half-bridge circuits in parallel respectively with theindividual batteries within the second string of individual batteries;forming a first leg of individual batteries by connecting the firststring of individual batteries in series with the second string ofindividual batteries; connecting the second string of individualbatteries in parallel with a second H-bridge circuit; commanding theupper switches within the second string half-bridge circuits to open andclose the upper switches within the second string half-bridge circuits.11. The method of claim 10, further comprising connecting second andthird legs of batteries in parallel with the first leg of batteries. 12.A non-transitory computer-readable medium tangibly embodyingcomputer-executable instructions of a program being executable by ahardware processor of a computing device with a user interface toprovide operations to: generate a plurality of triangle wave signals ata given amplitude and carrier frequency, each being phase-shifted fromthe other; generate a modulation signal for each of a plurality ofhalf-bridge circuits; compare an instantaneous magnitude of a respectiveindividual triangle wave signal to an instantaneous magnitude of arespective modulation signal; output a first command to an upper switchof a half-bridge circuit if the comparison is positive, and a secondcommand to the upper switch of a half-bridge circuit if the comparisonis negative; determine a respective modulation index for individualbatteries of a plurality of batteries based on a magnitude of eachrespective modulation signal and based on a magnitude of the respectiveindividual triangle wave signal; and regulates an amount of powercharged to and discharged from each individual battery by controllingeach respective modulation index for each half-bridge circuit, and bycontrolling the respective modulation signal with respect to therespective individual triangle wave signal for each individual battery,each modulation index based on a state-of-charge (SOC) of eachindividual and respective battery; wherein the plurality of individualbatteries are connected together in series into a first string ofindividual batteries, and the half-bridge circuits are connected inparallel to each of the plurality of individual batteries, eachhalf-bridge circuit having the upper switch and a lower switch, and afirst H-bridge circuit is connected in parallel with the first string ofindividual batteries.
 13. The medium of claim 12, wherein one of thefirst and second commands is to open the respective upper switch, andthe other of the first and second commands is to close the respectiveupper switch.
 14. The medium of claim 13, wherein the upper switch andthe lower switch operate complementary to one another.
 15. The medium ofclaim 12, wherein each battery has a respective state-of-charge (SOC)different from one another.
 16. The medium of claim 12, wherein themedium outputs commands to upper switches within the second stringhalf-bridge circuits to open and close the upper switches within thesecond string half-bridge circuits, wherein a first leg of batteriesincludes the first string of batteries connected in series with a secondstring of batteries, the second string of batteries connected in series,the second string of batteries having a second H-bridge circuitconnected in parallel and having respective second string half-bridgecircuits in parallel respectively with individual batteries within thesecond string of batteries.